The invention relates to a method and apparatus for imparting a permanent deformation to an elastic member made preferably from a coated web. More particularly, the invention relates to the permanent deformation of a coated web in a heated press. It has been previously proposed to apply heat during the deformation of a member made from a coated web. However, it has been found that after the parts of the elastic member had cooled off, the deformation imparted to the member deviated in an unpredictable way from the desired shape and location. When these deviations are combined with the unavoidable fluctuations in the quality of individual raw materials, the result becomes intolerable from the point of view of reliable use. The disadvantages of the known process are primarily due to the fact that, when the coated web is heated to for example 70.degree. C., it is subject to a contraction which is reversed when the web cools down, resulting in a return of the, for example, dish-shaped deformation of the part to a plane configuration.